Description
In the first part of the talk, the main aspects of the theory of zeta functions for compact, non abelian, group extensions of dynamical systems (mostly shifts of finite type) will be recalled. In particular, the link between the poles of twisted zeta functions and probabilistic phenomena will be recalled. We state some results for some non compact, non abelian group extensions of dynamical systems and discuss open problems for twisted zeta functions in the non compact, non abelian case.